GEOTEM: Geometric and Temporal ECG Models

A comprehensive framework for ECG classification that combines geometric theory, topological data analysis (TDA), and deep learning. This repository implements and compares three approaches:

• GTN: A novel Geometric-Temporal Network that leverages cross-attention among multiple geometric and topological signal representations
• CNN: Baseline 1D CNN with Grad-CAM visualization
• LSTM: Baseline LSTM with Integrated Gradients

Background & Novel Aspects

Geometric Signal Processing

ECG signals naturally exist on a geometric manifold where important features are invariant under certain transformations. Our approach leverages three key geometric aspects:

1. Discrete Curvature: Captures the local geometry of the signal through second-order variations, particularly effective for detecting P-waves and T-waves.

2. Geometric Phase: Represents the signal's dynamic evolution in phase space, making it particularly sensitive to rhythm abnormalities and morphological changes.

3. Topological Features: Uses persistent homology to capture multi-scale topological features, robust to noise and amplitude variations.

Cross-Attention Mechanism

The GTN model introduces a novel cross-attention mechanism that allows different geometric representations to interact:

Raw Signal ─┐
            │
Curvature ──┼─► Cross-Attention ─► Classification
            │
Phase ──────┤
            │
TDA Features┘

This architecture enables the model to:

• Learn which geometric features are most relevant for different ECG patterns
• Combine local and global geometric information
• Maintain interpretability through attention weights

Features

• Multi-scale Analysis: Combines features at different geometric scales
• Interpretability:
  • GTN: Cross-attention visualization
  • CNN: Grad-CAM for temporal importance
  • LSTM: Integrated Gradients for feature attribution
• Robust Evaluation:
  • 5-fold cross-validation
  • Statistical significance testing
  • Comprehensive metrics suite
• Visualization:
  • ROC curves with confidence intervals
  • Feature importance overlays
  • Confusion matrices
  • Metric comparisons

Installation

# Clone the repository
git clone https://github.com/salilp42/GEOTEM.git
cd GEOTEM

# Create a virtual environment (recommended)
python -m venv venv
source venv/bin/activate  # On Windows: .\venv\Scripts\activate

# Install dependencies
pip install -r requirements.txt

Project Structure

GEOTEM/
├── data/                    # Data directory
│   └── ECG200/             # ECG200 dataset
├── geotem/                 # Main package
│   ├── models/            # Model architectures
│   │   └── architectures.py  # GTN, CNN, LSTM implementations
│   ├── features/          # Feature extraction
│   │   └── geometric_features.py  # Geometric feature computation
│   ├── visualization/     # Plotting utilities
│   │   └── interpretability.py    # Model interpretation tools
│   └── utils/            # Helper functions
├── notebooks/             # Jupyter notebooks
├── scripts/              # Training scripts
│   └── train.py         # Main training pipeline
├── tests/               # Unit tests
└── results/            # Output directory

Usage

Basic Usage

from geotem.models import GTN_CrossAttention
from geotem.features import AdvancedGeometricFeatures

# Extract geometric features
feature_extractor = AdvancedGeometricFeatures()
X_geo = feature_extractor.extract_features(X_raw)

# Initialize and train GTN model
model = GTN_CrossAttention(
    N=sequence_length,
    out_channels=32,
    d_model=64,
    nhead=4
)

Training Pipeline

# Run full training pipeline with cross-validation
python scripts/train.py

Model Architecture Details

GTN (Geometric-Temporal Network)

• Input: 4-channel representation (raw, curvature, phase, TDA)
• Feature Processing: Independent CNN branches per channel
• Feature Interaction: Multi-head cross-attention
• Output: Binary classification through MLP

Baseline Models

• CNN: 1D convolutions with max pooling
• LSTM: Bidirectional LSTM with final state classification

Results

Hold-out Test Set Performance

Performance metrics on the ECG200 test set:

Model	Accuracy	Precision	Recall	F1-Score	AUC-ROC	MCC
GTN	0.8700	0.8806	0.9219	0.9008	0.9158	0.7142
CNN	0.8300	0.8730	0.8594	0.8661	0.9188	0.6335
LSTM	0.6600	0.6829	0.8750	0.7671	0.7214	0.1909

Statistical Analysis

Pairwise Wilcoxon tests on 5-fold cross-validation metrics to assess statistical significance:

GTN vs CNN

• Accuracy: p=0.0679
• Precision: p=0.0625
• Recall: p=0.4142
• F1-score: p=0.1250
• AUC-ROC: p=0.4375
• MCC: p=0.0625

GTN vs LSTM

• Accuracy: p=0.1250
• Precision: p=0.1250
• Recall: p=0.4142
• F1-score: p=0.1250
• AUC-ROC: p=0.1250
• MCC: p=0.1250

CNN vs LSTM

• Accuracy: p=1.0000
• Precision: p=0.3125
• Recall: p=0.1441
• F1-score: p=0.8125
• AUC-ROC: p=0.3125
• MCC: p=0.6250

Key Findings

1. GTN Performance:

   • Best overall performance on test set (Accuracy: 87%, F1: 0.90)
   • Highest precision (0.88) and recall (0.92)
   • Strong MCC score (0.71) indicating reliable predictions

2. Model Comparison:

   • GTN shows marginally significant improvements over CNN in accuracy, precision, and MCC
   • Both GTN and CNN substantially outperform LSTM
   • High AUC-ROC scores for GTN (0.92) and CNN (0.92) suggest excellent discrimination ability

3. Statistical Significance:

   • Most pronounced differences between GTN and CNN (p < 0.07 for key metrics)
   • Less significant differences between CNN and LSTM
   • Results suggest GTN's geometric features provide meaningful improvements

Note: Statistical tests performed on 5-fold CV results; p-values < 0.05 considered significant, < 0.10 marginally significant

Citation

If you use this code in your research, please cite:

@software{patel2024geotem,
  author = {Patel, Salil},
  title = {GEOTEM: Geometric and Temporal ECG Models},
  year = {2024},
  publisher = {GitHub},
  url = {https://github.com/salilp42/GEOTEM}
}

Contributing

Contributions are welcome! Please feel free to submit a Pull Request. Areas of particular interest:

• Additional geometric features
• New attention mechanisms
• Performance optimizations
• Extended documentation

License

This project is licensed under the MIT License - see the LICENSE file for details.

Author

Salil Patel